A Multivariate Additive Inflation Approach to Improve Storm‐Scale Ensemble‐Based Data Assimilation and Forecasts: Methodology and Experiment With a Tornadic Supercell.

Ensemble‐based convective‐scale radar data assimilation commonly suffers from an underdispersive background ensemble. This study introduces a multivariate additive‐inflation method to address such deficiency. The multivariate additive inflation (AI) approach generates coherent random perturbations drawn from a newly constructed convective‐scale static background error covariance matrix for all state variables including hydrometeors and vertical velocity. This method is compared with a previously proposed univariate AI approach, which perturbs each variable individually without cross‐variable coherency. Comparisons are performed on the analyses and forecasts of the 8 May 2003 Oklahoma City tornadic supercell. Within assimilation cycles, the multivariate approach is more efficient in increasing reflectivity spread and thus has a reduced spinup time than the univariate approach; the additional inclusion of hydrometeors and vertical velocity results in more background spread for both reflectivity and radial velocity. Significant differences among AI experiments also exist in the subsequent forecasts and are more pronounced for the forecasts initialized from the earlier assimilation cycles. The multivariate approach yields better forecasts of low‐level rotation, reflectivity distributions, and storm maintenance for most lead times. The additional inclusion of hydrometeor and vertical velocity in the multivariate method is beneficial in forecasts. Conversely, the additional inclusion of hydrometeor and vertical velocity in the univariate method poses negative impacts for the majority of forecast lead times. Plain Language Summary: Data assimilation (DA) requires an accurate estimation of the background uncertainty. In ensemble‐based DA, such uncertainty is represented by the statistics of a background ensemble. However, it is difficult to construct ideal background ensembles that truly represent forecast errors. The deficient background ensemble becomes more problematic for convective‐scale radar DA when all ensemble members miss the observed storms. This study proposes a multivariate additive‐inflation approach to address such deficiency. The mitigation of ensemble deficiency is achieved by drawing spatially and physically coherent random perturbations from a recently constructed convective‐scale static background error covariance matrix and adding them to each ensemble member. This study assesses the new approach by comparing it with a previously proposed univariate approach, which perturbs each variable individually without cross‐variable coherency. Results and diagnostics from a tornadic supercell study show that the multivariate approach improves the analysis and forecast compared to the univariate approach. The multivariate approach by additionally perturbing hydrometeors and vertical velocity further improves the forecast. In contrast, the univariate approach including the hydrometeors and vertical velocity perturbations degrades the forecast. Key Points: A multivariate additive‐inflation approach is introduced to address the deficient ensemble for ensemble‐based radar data assimilationThe multivariate approach improves the analysis and forecast of a tornadic supercell relative to a previous univariate approachThe multivariate approach by additionally perturbing hydrometeors and vertical velocity is beneficial in analysis and forecast [ABSTRACT FROM AUTHOR]